There is a widespread need in basic biomedical research as well as in applications such as drug delivery and biotechnology for micro-motors that can generate translational motions or induce local strains on cellular or molecular length scales. For example, many areas of biological research involve the application of forces to individual cells or even macromolecules; nanoscale chemistry requires the rapid and directed transport of reagents between compartments in microreactors; and targeted drug delivery is a major aim in the pharmaceutical industry.
The past few decades have seen increased interest in low Reynolds number swimming mechanisms with research along two complementary lines. Firstly, the need to understand how micrometer-sized organisms are able to propel themselves in a world with no inertia has led to important insights, for example the discovery and analysis of the rotating bacterial flagella. The second line is more utilitarian, and aimed at the construction of autonomous microrobots, capable of performing useful functions such as active targeted drug delivery, destroying kidney stones [J. Edd et al. in Proc. IEEE/RSJ Int. Conf. Intelligent Robots and Systems (2003), vol. 3, pp. 2583-2588] or stirring and pumping in microfluidic devices [S. T. Chang et al., Nature Materials 6, 235 (2007)].
A very nice introduction to the physics of motion at low Reynolds number can be found in E. M. Purcell, Am. J. Phys 45, 3 (1977). Broadly speaking the Reynolds number defines the ratio of inertial forces to viscous forces for an object moving through a fluid. The techniques we describe for swimming in a fluid at low Reynolds number preferably relate to a Reynolds number of less than 1, more typically of order 10−3, 10−4, or 10−5. This compares with the Reynolds number for, say, a man swimming in water which is of order 104. In a low Reynolds number environment intuitions about the nature and mechanism of motion are generally wrong, in part because inertia is essentially irrelevant. For example a reciprocal motion, that is one in which a body deforms and then returns to the original shape by going through the deformation in reverse does not result in translation through the fluid. This has been termed the “scallop theorem”—a scallop cannot swim at low Reynolds number because it only has one hinge and is thus bound to make a reciprocal motion. For non-reciprocal motions, which break the time-reversal symmetry, translational motion (swimming) can occur although the direction is often counter-intuitive.
A low Reynolds number swimmer, natural or artificial has two requirements in order to propel itself through the fluid environment. The first is related to the peculiar restrictions arising from the fact that for micrometer-sized swimmer in aqueous environments the fluid flow is dominated by viscous effects. This situation is best illustrated by the aforementioned “scallop theorem”; the trajectory of the swimmer is determined by the sequence of geometrical configurations it assumes (time makes no difference: the pattern of motion is the same whether the change is fast or slow). Self-propulsion is only possible if forward- and backward-motion phases in a full swimming cycle are non-reciprocal, that is not symmetric with respect to time reversal (the motion looks different depending whether it is “played” forwards or backwards). The system should have at least two degrees of freedom in its configurational space or it will perform a reciprocal motion with no net translation. As a result effort has been invested in devising various shape sequences that would lead to translational motion [S. Camalet et al., Phys. Rev. Lett. 82, 1590 (1999); L. E. Becker et al., J. Fluid Mech. 490, 15 (2003); A. Najafi and R. Golestanian, Phy. Rev. E. 69, 062901 (2004); and J. E. Avron et al. New J. Phys. 7, 234 (2004)] and analysing the efficiency of swimming [A Shapere and F. Wilczek, J. Fluid Mech. 198, 557 (1989), ibid 198, 587 (1989); E. M. Purcell, Proc. Natl. Acad. Sci. USA 94, 11307 (1997); J. E. Avron et al., Phys. Rev. Lett. 93, 186001 (2004); D. Tamand A. E. Hosoi, Phys. Rev. Lett. 98, 068105 (2007)].
However this is only part of the problem. The second requirement for a successful swimmer is an actuation mechanism for generating the shape sequence, and the requisite energy. This question still remains largely unresolved, with a few proposed mechanisms holding promise, such as mechano-chemical coupling in elastic membranes [R. Lipowsky, in Statistical Mechanics of Biocomplexity (Springer, Berlin, 1999), vol. 527 of Lecture Notes in Phys., pp. 1-23; P. G. Petrov et al. Europhys Lett. 48, 435 (1999)] or the use of magnetic [K. Ishiyama et al. Sens. Actuators, A 91, 141 (2001)] or electric fields [S. T. Chang et al., Nature Materials 6, 235 (2007); Y. Osada et al., Nature 355, 242 (1992)]. Plagiarising from nature is of little help here: the flagellar rotor, for example is an extremely sophisticated piece of machinery, consisting of over 20 components packed in a tiny volume, which is impossible to reproduce with current technology.
Thus there has been a search for simpler mechanisms. The inventors have previously described “Ferromagnetic dipole-pair tweezers for biomedical applications”, F. Y. Ogrin, C. P. Winlove and P. G. Petrov, at the joint 10th MMM/Intermag Conference in Baltimore in 2007, 7-11 Jan. and speculated that these might be used for swimming. However the inventors later discovered that the device they described would not work as a swimming device. An interesting theoretical approach is described in Najafi et al. (ibid). A practical swimming device has been described in a number of papers by Ishiyama and colleagues (ibid) and also, for example, T. Honda, K. I. Arai, K. Ishiyama, “Micro swimming mechanisms propelled by external magnetic fields,” IEEE Trans. Magnetics, vol 32, issue 5, pp. 5085-5087, September 1996; IEEE Trans. Magnetics, vol. 41, No. 10, pp. 4012-4014, pp. 4021-4023 and pp. 4191-4193 (2005) and JP 2001-179700. Broadly speaking this device comprises a magnet attached to a helical of wire which is propelled through a medium by magnetic torque. The first artificial microswimmer with a flexible flagellum-like tail has also recently been assembled [R. Dreyfus et al., Nature 437, 862 (2005). However, it is still a complicated assembly of magnetic particles bridged by DNA molecules and attached to a red blood cell, which makes the routine production of this type of swimmers untenable. Further background prior art can be found in US 2006/196301 and US 2005/029978.
There is, however, a need for improved microrobotic magnetic devices, in particular for swimming through a medium at low Reynolds number, for example for transporting material or, say, performing surgery.